A crisis in the Belousov-Zhabotinskii reaction: Experiment and simulation

An abrupt transition that has the character of aninterior crisis was observed in an experiment on the Belousov-Zhabotinskii reaction as a control parameter was varied (a crisis is a qualitative change in the dynamics of a system observed when an attractor collides with the stable manifold of a fixed point). The interpretation of the observed behavior as a crisis is corroborated by a numerical analysis of a seven-variable model of the reaction. The waveforms, attractors, and maps obtained in the simulation are remarkably similar to those obtained in the laboratory experiment. The simulation indicates that the crisis is a consequence of a multivalued first return map.

[1]  H. Swinney,et al.  Alternating periodic and chaotic regimes in a chemical reaction — Experiment and theory , 1981 .

[2]  A. Arneodo,et al.  From quasiperiodicity to chaos in the Belousov–Zhabotinskii reaction. II. Modeling and theory , 1987 .

[3]  R. W. Rollins,et al.  Intermittent transient chaos at interior crises in the diode resonator , 1984 .

[4]  Françoise Argoul,et al.  From quasiperiodicity to chaos in the Belousov–Zhabotinskii reaction. I. Experiment , 1987 .

[5]  Argoul,et al.  Type-II intermittency in a peroidically driven nonlinear oscillator. , 1986, Physical review. A, General physics.

[6]  Glorieux,et al.  Laser chaotic attractors in crisis. , 1986, Physical review letters.

[7]  M. Feigenbaum.  Quantitative universality for a class of nonlinear transformations , 1978 .

[8]  Grebogi,et al.  Critical exponent of chaotic transients in nonlinear dynamical systems. , 1986, Physical review letters.

[9]  J. Roux,et al.  Experimental observations of complex dynamical behavior during a chemical reaction , 1981 .

[10]  A. Arneodo,et al.  The periodic-chaotic sequences in chemical reactions: A scenario close to homoclinic conditions? , 1985 .

[11]  J. Ginocchio.  On a generalization of quasispin to monopole and quadrupole pairing , 1979 .

[12]  Raymond Kapral,et al.  Bifurcation phenomena near homoclinic systems: A two-parameter analysis , 1984 .

[13]  Harry L. Swinney,et al.  Testing nonlinear dynamics , 1984 .

[14]  Hilborn.  Quantitative measurement of the parameter dependence of the onset of a crisis in a driven nonlinear oscillator. , 1985, Physical review. A, General physics.

[15]  Nicholas C. Metropolis,et al.  On Finite Limit Sets for Transformations on the Unit Interval , 1973, J. Comb. Theory A.

[16]  James A. Yorke,et al.  Metastable chaos: The transition to sustained chaotic behavior in the Lorenz model , 1979 .

[17]  Françoise Argoul,et al.  Experimental evidence for homoclinic chaos in the Belousov-Zhabotinskii reaction , 1987 .

[18]  Y. Ueda.  EXPLOSION OF STRANGE ATTRACTORS EXHIBITED BY DUFFING'S EQUATION , 1979 .

[19]  James P. Crutchfield,et al.  Chaotic States of Anharmonic Systems in Periodic Fields , 1979 .

[20]  J. L. Hudson,et al.  An experimental study of multiple peak periodic and nonperiodic oscillations in the Belousov–Zhabotinskii reaction , 1979 .

[21]  Pierre Coullet,et al.  ITÉRATIONS D'ENDOMORPHISMES ET GROUPE DE RENORMALISATION , 1978 .

[22]  C. Vidal,et al.  Non-Equilibrium Dynamics in Chemical Systems , 1984 .